Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #23781426 | C2 | semidirect |
| 5. #23781424 | C2 | semidirect |
| 6. #23781421 | C2 | semidirect |
| 7. H(3,ℤ/4)×C163 | C2 | semidirect |
| 14. #19104692 | C4 | semidirect |
| 16. C42×D163 | C4 | semidirect |
| 102. C163 | #1827 | semidirect |
| 110. H(3,ℤ/4) | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782133 | 2 |
| #23781647 | 2 |
| #23781638 | 2 |
| #23781426 | 2 |
| #23781424 | 2 |
| #23781421 | 2 |
| H(3,ℤ/4)×C163 | 2 |
| #1827 | 163 |